Collision Theory
Factors Affecting Rate In order for a reaction to occur, two particles must collide. Therefore, any factors that change how these particles collide will change the rate of the reaction. All of the factors listed below change collision frequency in some way. Physical State This factor is all about contact of one substance with another. If one is a solid while another is a gas, there will be very little contact. Since the atoms within the solid crystalline can only vibrate in place, the gas particles will only interact with the surface of the solid particles. This is why physical state matters; in order for the substances to mix effectively and thus collide, they must be the same state of matter. Surface Area Surface area impacts reaction rate for a similar reason as physical state because it involves how much contact each substance has with one another. In very fine particles, much of the surface of a solid substance is exposed to the other substance, therefore there are more atoms that can react with each other. Concentration Since concentration is amount of molecules per unit of volume, changing concentration changes the amount of molecules that are able to undergo a reaction. If there are more molecules that can react, there will be more collisions on average, and the rate of the reaction will increase. Temperature (most important!) Temperature is by far the most important factor affecting the reaction rate due to the corresponding increase in kinetic energy in the particles. Temperature is proportional to the average kinetic energy, so increasing temperature increases the average speed of movement, so more collisions will happen. In addition, to break the intramolecular forces of each substance, a sufficient amount of energy is required. Temperature changes the fraction of molecules that have enough energy to react. This arbitrary amount of energy that a molecule must have to react is called the activation energy (Ea). ' '''As seen by the diagram to the right, even though the temperature is only increased by ten degrees, the number of molecules that have more energy than the activation energy (shown by the dotted line) is significantly more. This is why temperature has such a big impact on the reaction rate. Collision Theory The main purpose of understanding collision theory is to understand how the general form of a rate law was derived. Since reactants must collide, upon first glance, the possible number of collisions appears to be the sum of the number of total reactants. So, with a reaction of A + B --> C, 3 particles of A and 2 particles of B might appear to have 5 possible collisions. However, there are six because each particle of A can react with either two particles of B. For this reason, the rate law requires multiplication of concentrations together. Particles with higher order reaction orders are multiplied into the rate law multiple times, and therefore with simplification become exponents. Activation Energy With a shallow look at the general form for a rate law, it is not clear that temperature has any effect whatsoever on the rate, only concentration. '''Rate = k∙AmBnCp' Where A, B, and C are reactants, and m, n, and p are reaction orders (must be integers) However, as explained earlier, temperature has a very big effect on the rate, so where does temperature fit into this equation? It turns out that temperature is one of the determinants of the rate constant value. However, there are other factors that give the graph of rate constant v. time an exponential form. Svante Arrhenius related these together in his Arrhenius equation, stated below: k = A∙e-Ea/RT where A = the frequency factor Note: Temperature here is absolute temperature, make sure that you don't plug in the temperature in Celsius! The frequency factor depends on two other factors, the orientation probability factor (p) '''and '''collision frequency (Z). The orientation probability factor is the ratio of effective collisions (collisions in which the reaction occurs) to possible collisions, assuming there is enough energy. It depends largely on the complexity of the reactants. For molecules, the orientation probability factor could be very low, like 0.006 for nitric oxide and nitrogen trioxide, or close to 1 for single atoms. By taking the natural log of both sides, you can linearize the graph and calculate the activation energy. ln ''k ''= – (Ea/R)(1/T) + ln A The slope of the graph is equal to – Ea/R Note: Since we’re dealing with energy, the gas constant is 8.314 J/mol∙K. In addition, watch out for units (J versus kJ) If you don't have a graph and instead have a couple k'' values at certain temperatures, you can calculate the activation energy in the same manner as before. '''ln ''k2/k1 = -(Ea/R)(1/T2-1/T1)'''